Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Commutative Ideals in BE-algebras

  • Received : 2011.07.18
  • Accepted : 2012.05.03
  • Published : 2012.12.23
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Abstract

In this paper we study properties of commutative BE-algebras and we give the construction of quotient (X/I; *, I) of a commutative BE-algebra X via an obstinate ideal I of X. We construct upper semilattice and prove that is a nearlattice. Finally we define and study commutative ideals in BE-algebras.

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References

  1. S. S. Ahn and K. S. So, On generalized upper sets in BE-Algebras, Bull. Korean Math. Soc., 46(2)(2009), 281-287. https://doi.org/10.4134/BKMS.2009.46.2.281
  2. S. S. Ahn and K. S. So, On ideals and upper sets in BE-algebras, Sci. Math. Jpn., 68(2)(2008), 279-285.
  3. I. Chajda, R. Halas And J. Kuhr, Semilattice Structures, Heldermann Verlag, Germany, 2007.
  4. Y. Huang, BCI-algebra, Science Press, Beijing, China, 2006.
  5. Y. Imai and K. Iseki, On axiom systems of propositional Calculi, XIV Proc. Jpn. Academy, 42(1966), 19-22. https://doi.org/10.3792/pja/1195522169
  6. H. S. Kim and Y. H. Kim, On BE-Algebras, Sci. Math. Japon, Online e-2006, 1299-1302.
  7. B. L. Meng, On Filters in BE-algebras, Sci. Math. Japon, Online, e-2010, 105-111.
  8. A. Rezaei and A. Borumand Saeid, On fuzzy subalgebras of BE-algebras, Afrika Matematika, 22(2)(2011), 115-127. https://doi.org/10.1007/s13370-011-0011-4
  9. A. Rezaei, Congruencec relations on BE-algebras, 3th Math. Sci. Con. of PNU, Mashhad, Iran, (2010), 57-64.
  10. A. Rezaei and A. Borumand Saeid, Some results on BE algebras, Analele Universitatii Oradea Fasc. Matematica, Tom XIX (2012), 33-44.
  11. S. Z. Song, Y. B. Jun and K. J. Lee, Fuzzy Ideals in BE-algebras, Bull. Malays. Math. Sci. Soc., 33(2010), 147-153.
  12. A. Walendziak, On commutative BE-algebras, Sci. Math. Japon, Online, e-2008, 585-588.

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  2. δ-relation on dual hyper K–algebras vol.29, pp.5, 2015, https://doi.org/10.3233/IFS-151667
  3. Some Types of Filters in BE-algebras vol.7, pp.3, 2013, https://doi.org/10.1007/s11786-013-0157-6